James' Submodule Theorem and the Steinberg Module

Symmetry Integrability and Geometry-Methods and Applications

article

Meinolf Geck¹ 

[1] IAZ - Lehrstuhl für Algebra, Universität Stuttgart

关键词: groups with a BN-pair;    Steinberg representation;    modular representations;   

DOI  :  10.3842/SIGMA.2017.091

来源: National Academy of Science of Ukraine

【 摘 要 】

James' submodule theorem is a fundamental result in the representation theory of the symmetric groups and the finite general linear groups. In this note we consider a version of that theorem for a general finite group with a split $BN$-pair. This gives rise to a distinguished composition factor of the Steinberg module, first described by Hiss via a somewhat different method. It is a major open problem to determine the dimension of this composition factor.

【 授权许可】

Unknown